New United boss, Jose Mourinho, has been desperately looking for a new attacker to lead the line in his United revolution, and has targeted the Armenian, who only has one year left on his contract at the Signal Iduna Park.
The German side have proven stubborn to even consider a deal, having already lost both Matt Hummels and İlkay Gündoğan this summer.
However it does seem that they are resigned to losing their midfielder, who managed 18 goals and 25 assists last season, with United upping their bid to around £26million.
All to be decided
Thomas Tuchel's side are expected to return for pre-season training next Monday, and the club's CEO, Hans-Joachim Watzke, has said the decision on his future is imminent.
He told Kicker that they will "assess his situation" in the next week with sporting director Michael Zorc and coach Tuchel but admitted that it is a "difficult decision".
Watzke continued, saying that there are "three perspectives" with "every transfer" which is "economical" a "strategic" and "sporting". If the economical sides become "overwhelming" then it could force someone to make a "different decision in the end".
United have only made the one signing so far, with the capture of Villarreal defender, Eric Bailly.
But along with the potential deal for Mkhitaryan, it is also expected that United will complete the signing of PSG striker, Zlatan Ibrahimovic, within the next week.
It is reported that the Swede completed personal terms, on a one-year contract, prior to Euro 2016, and the deal is expected to be completed following a successful medical.
Manchester United will take on Leicester City in the Community Shield, at Wembley Stadium, on Sunday, August 7.